Bottom Line:
Applying the proposed method to exemplary datasets and comparing each brain signal with both sex hormones signals, we found a characteristic profile of coincident periods and typical relative phases.Findings suggest that the procedure applied here provides a method to analyze typical frequencies, or periods and phases between signals with the same period.It generates specific patterns for brain signals and hormones and relations among them.

Background: Fourier transform is a basic tool for analyzing biological signals and is computed for a finite sequence of data sample. The electroencephalographic (EEG) signals analyzed with this method provide only information based on the frequency range, for short periods. In some cases, for long periods it can be useful to know whether EEG signals coincide or have a relative phase between them or with other biological signals. Some studies have evidenced that sex hormones and EEG signals show oscillations in their frequencies across a period of 28 days; so it seems of relevance to seek after possible patterns relating EEG signals and endogenous sex hormones, assumed as long time-periodic functions to determine their typical periods, frequencies and relative phases.

Methods: In this work we propose a method that can be used to analyze brain signals and hormonal levels and obtain frequencies and relative phases among them. This method involves the application of a discrete Fourier Transform on previously reported datasets of absolute power of brain signals delta, theta, alpha1, alpha2, beta1 and beta2 and the endogenous estrogen and progesterone levels along 28 days.

Results: Applying the proposed method to exemplary datasets and comparing each brain signal with both sex hormones signals, we found a characteristic profile of coincident periods and typical relative phases. For the corresponding coincident periods the progesterone seems to be essentially in phase with theta, alpha1, alpha2 and beta1, while delta and beta2 go oppositely. For the relevant coincident periods, the estrogen goes in phase with delta and theta and goes oppositely with alpha2.

Conclusion: Findings suggest that the procedure applied here provides a method to analyze typical frequencies, or periods and phases between signals with the same period. It generates specific patterns for brain signals and hormones and relations among them.

Figure 1: Intensity of the different brain signals superimposed to hormone level signals. The horizontal scale is 2π/28 days-1. The vertical scale has normalized arbitrary units. It is shown period coincidences and relative intensities in different points; when the peaks agree and both are bigger than 1/3 the coincidences were taken into account for this analysis, considering the smaller peaks as noise generated from the discrete Fourier transform.

Mentions:
The transformed signals are plotted in Figure 1 against frequency in units of 2π/28 days-1. The frequency patterns for each one of the EEG-signals and the two hormone levels are plotted below for positive values of the frequencies. As it can be seen, each one of these eight signals presents a peculiar pattern, a characteristic spectrum, each one in different color and normalized to 1. In blue are plotted the estrogen signals; in red, the progesterone signals; in green, the brain signals. In (a), according to the selection criterion, the spectrum of the delta brain signal versus estrogen shows a coincidence in 4; versus progesterone, a coincidence in 2. In (b), the spectrum of the theta brain signal versus estrogen shows a coincidence in 4; versus progesterone, a coincidence in 3. In (c), the spectrum of the alpha1 brain signal versus estrogen shows non coincidence; versus progesterone, a coincidence in 2 and 3. In (d), the spectrum of the alpha2 brain signal versus estrogen shows a coincidence in 1; versus progesterone, a coincidence in 1, 2, and 3. In (e), the spectrum of the beta1 brain signal versus estrogen shows non coincidence; versus progesterone, a coincidence in 2 and 3. In (f), the spectrum of the beta2 brain signal versus estrogen shows non coincidence; versus progesterone, a coincidence in 3. The Fourier transform of each brain signal and hormone levels were plotted superimposed each other, to analyze relative phases between them. When one of the relevant brain signal periods essentially coincides with one of the hormone levels, the relative phase between the two corresponding time functions is displayed in Figure 2 and Figure 3. It should be remarked that the phases presented in each one of these figures correspond to the relevant trigonometric components of the whole signal, centered around the frequency of interest, for we have related coincident relevant frequencies of the two signals considered.

Figure 1: Intensity of the different brain signals superimposed to hormone level signals. The horizontal scale is 2π/28 days-1. The vertical scale has normalized arbitrary units. It is shown period coincidences and relative intensities in different points; when the peaks agree and both are bigger than 1/3 the coincidences were taken into account for this analysis, considering the smaller peaks as noise generated from the discrete Fourier transform.

Mentions:
The transformed signals are plotted in Figure 1 against frequency in units of 2π/28 days-1. The frequency patterns for each one of the EEG-signals and the two hormone levels are plotted below for positive values of the frequencies. As it can be seen, each one of these eight signals presents a peculiar pattern, a characteristic spectrum, each one in different color and normalized to 1. In blue are plotted the estrogen signals; in red, the progesterone signals; in green, the brain signals. In (a), according to the selection criterion, the spectrum of the delta brain signal versus estrogen shows a coincidence in 4; versus progesterone, a coincidence in 2. In (b), the spectrum of the theta brain signal versus estrogen shows a coincidence in 4; versus progesterone, a coincidence in 3. In (c), the spectrum of the alpha1 brain signal versus estrogen shows non coincidence; versus progesterone, a coincidence in 2 and 3. In (d), the spectrum of the alpha2 brain signal versus estrogen shows a coincidence in 1; versus progesterone, a coincidence in 1, 2, and 3. In (e), the spectrum of the beta1 brain signal versus estrogen shows non coincidence; versus progesterone, a coincidence in 2 and 3. In (f), the spectrum of the beta2 brain signal versus estrogen shows non coincidence; versus progesterone, a coincidence in 3. The Fourier transform of each brain signal and hormone levels were plotted superimposed each other, to analyze relative phases between them. When one of the relevant brain signal periods essentially coincides with one of the hormone levels, the relative phase between the two corresponding time functions is displayed in Figure 2 and Figure 3. It should be remarked that the phases presented in each one of these figures correspond to the relevant trigonometric components of the whole signal, centered around the frequency of interest, for we have related coincident relevant frequencies of the two signals considered.

Bottom Line:
Applying the proposed method to exemplary datasets and comparing each brain signal with both sex hormones signals, we found a characteristic profile of coincident periods and typical relative phases.Findings suggest that the procedure applied here provides a method to analyze typical frequencies, or periods and phases between signals with the same period.It generates specific patterns for brain signals and hormones and relations among them.

Background: Fourier transform is a basic tool for analyzing biological signals and is computed for a finite sequence of data sample. The electroencephalographic (EEG) signals analyzed with this method provide only information based on the frequency range, for short periods. In some cases, for long periods it can be useful to know whether EEG signals coincide or have a relative phase between them or with other biological signals. Some studies have evidenced that sex hormones and EEG signals show oscillations in their frequencies across a period of 28 days; so it seems of relevance to seek after possible patterns relating EEG signals and endogenous sex hormones, assumed as long time-periodic functions to determine their typical periods, frequencies and relative phases.

Methods: In this work we propose a method that can be used to analyze brain signals and hormonal levels and obtain frequencies and relative phases among them. This method involves the application of a discrete Fourier Transform on previously reported datasets of absolute power of brain signals delta, theta, alpha1, alpha2, beta1 and beta2 and the endogenous estrogen and progesterone levels along 28 days.

Results: Applying the proposed method to exemplary datasets and comparing each brain signal with both sex hormones signals, we found a characteristic profile of coincident periods and typical relative phases. For the corresponding coincident periods the progesterone seems to be essentially in phase with theta, alpha1, alpha2 and beta1, while delta and beta2 go oppositely. For the relevant coincident periods, the estrogen goes in phase with delta and theta and goes oppositely with alpha2.

Conclusion: Findings suggest that the procedure applied here provides a method to analyze typical frequencies, or periods and phases between signals with the same period. It generates specific patterns for brain signals and hormones and relations among them.